Is expiation obligatory for one who put a cat out of the house, and it died due to the cold? And is that considered killing a soul?

The Islamic texts indicate that there is a reward for showing kindness to animals that are deemed worthy of respect. As for animals that are commanded to be killed by Islamic law, the command of the Law should be fulfilled by killing them. There is no sin upon you for putting the cat outside the house, because sin lies in confining it without feeding it, and you have fed it and not confined it.